Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20

Topic

Linear Functions

Description

This image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4.

This example showcases a linear function with a positive fractional slope, demonstrating how to work with fractions in both the slope calculation and the final equation. It reinforces the importance of precise calculations and fraction simplification in mathematics. Understanding how to manipulate fractions in linear functions is crucial for students as they progress to more advanced mathematical concepts.

Exposure to various types of linear functions, including those with fractional components, is essential for building a strong foundation in algebra. This example helps students develop their skills in fraction manipulation and reinforces the connection between graphical representations and algebraic equations. Such practice is invaluable for developing mathematical fluency and problem-solving abilities across different contexts.

Teacher's Script: In our final example, we're working with a fractional slope again, but this time it's positive. Notice how we carefully calculate our slope and use it in the point-slope form. When we simplify our equation, we end up with fractions. This is a great opportunity to practice your fraction simplification skills! Remember, in many cases, leaving your answer as a fraction is more precise than converting to a decimal. Think about why this might be important in real-world applications.

For a complete collection of math examples related to Linear Functions click on this link: Math Examples: Linear Functions Collection.